An isolated system consists of two rigid subsystems of volumes V₁ and V₂ separated by a rigid and porous membrane. Helium (He) can diffuse through the membrane, but oxygen (O₂) cannot.We label the gases as A for helium and B for oxygen. The whole system is in thermal equilibrium at all times. Each gas can be considered an idealsystem is divided into two by an osmotic membrane which lets substance A diffuse through it, but not substance B. gas, i.e. they satisfy the equations of state (5.46) and (5.47), namely, pV = NR T and U = cNRT. The gas mixture obeys the ideal mixture relation (8.68), that is,where μ_A (T, p) and μ_B (T, p) are the chemical potentials of substances A and B when they are pure, c_A and c_B are the concentrations of A and B. Initially, the system contains N₀ moles of helium in subsystem 1, and N_B moles of oxygen in subsystem 2 (Fig. 8.6). The numbers of moles N₀ and N_B are chosen so that the initial pressure p_i is the same in both subsystems. At all times, each subsystem is assumed to be homogeneous. Designate by N₁ and N₂ the number of moles of helium in subsystems 1 and 2, respectively.a) At equilibrium, show that μ_A (T, p₁) = μ_A (T, p₂, c_A).b) Deduce from the previous result a relation between the pressures p₁ and p₂ when the two sub-systems reach equilibrium. Express c_A, p₁ and p₂ in terms of N₂. Determine p₁ and p₂ in terms of the initial pressure pi under the condition of equal volume, i.e. V₁ = V₂ = V₀.

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A: No Initial B: NB Pressure: Pi Pressure: Pi 1 Final A:No-N₂ A: B: N₂ NB Pressure: P₁ Pressure: P2